Analyzing Concavity of a Function
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Second Derivative: Concavity
by
Eddie W.
Key Questions

For a quadratic function
#f(x)=ax^2+bx+c# ,
if#a>0# , then#f# is concave upward everywhere,
if#a<0# , then#f# is concave downward everywhere. 
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Questions
Videos on topic View all (3)
Graphing with the Second Derivative

1Relationship between First and Second Derivatives of a Function

2Analyzing Concavity of a Function

3Notation for the Second Derivative

4Determining Points of Inflection for a Function

5First Derivative Test vs Second Derivative Test for Local Extrema

6The special case of x⁴

7Critical Points of Inflection

8Application of the Second Derivative (Acceleration)

9Examples of Curve Sketching